A game on a graph

Two players, Askar and Bob, play a game with a token on an undirected graph G. The game goes as follows: - Askar chooses a starting vertex and places the token on this vertex. - The players now alternate turns; Bob moves first. - In his turn, each player has to move the token along exactly one edge to another vertex. - It's not allowed to move the token to some vertex if it was on that vertex